Rank and Relative Rank of Each Ideal of the Semigroup DO_n
Luo Yong-gui · Journal of Jilin University(Science Edition) · 2013
Let DOn be the semigroup of all order-reversing singular transformations on a finite-chain [n].For an arbitrary integer r(1≤r≤n-1),the rank of semigroup LD(n,r)={α∈DOn: Im α≤r} was studied.We proved that LD(n,r) is generated by elements of rank r,with rank being Crn.Furthermore,it is shown that the relative rank of the semigroup LD(n,r) with respect to itself each ideal LD(n,l) is equal to Crn if 1≤lr.